I have a building that will be powering 4 shop lights and 4 outlets. Things that are plugged in are air conditioner 110v 5000btu, radio, occasionally air compressor, other power tools(nothing big), and smaller things. I went to ace to get supplies and ask what I needed and was told I need a 30 amp sub panel ran to the shed with 10-2 or 10-3 wire ran from the main breaker panel (house). I was given a 15amp and two 20 amp breakers for the sub panel, 15 to power the lights, one of the 20’s for all the outlets, and the other 20 for the air conditioner. Does all this sound correct? I need to know if it is then do I need to wire strictly all the outlets (besides the one powering the AC) to the 20amp breaker and all the lights to the 15amp breaker? And the last 20amp breaker to the AC alone? Thanks in advance.
Scrimping now will hit you in the pocketbook far harder later on
Your problem is that you're so focused on pinching pennies right now that you don't realize just how much undoing and redoing your work later when you inevitably run out of room (either amps or spaces) will cost you. Most of the cost in running power to an outbuilding is in trenching, so it's far better to spend a little extra on materials now so that you room for expansion later than it is to back yourself into the proverbial corner now.
First off, direct bury cable is never a good deal in the long run, as you have to dig it up if you want more power at the shed down the road, and that's terribly expensive. It's far better to put in a pair of Schedule 80 PVC conduits now, one 1.5" or 2" for power and another 1" for future telephone or data service, so that you'll only ever have to trench to the shed once for this sort of thing, no matter what you want there for electricity, networking, and so on. Furthermore, you don't need to trench quite as deep if you put conduit in -- 21-22" for PVC conduit, vs the about 25" deep trench you'll need to get 24" of cover over a direct buried cable.
Inside that conduit, by the way, you won't be pulling any cables either. Instead, you will be pulling individual THHN/THWN wires inside that conduit: 4 10AWG stranded wires (black, black or red, white, green or bare) will suffice for now, and the fat conduit both makes for an easy pull now, compared to wrestling a 10/3 UF alligator down the conduit, and gives you plenty of room to expand later on.
You don't have the space you think you do!
Furthermore, your subpanel is far too small to provide any useful expansion room for your shed, especially if you wind up wanting 240V tools there in the future. This is partially because you're not accounting for the need to have a two-pole breaker in the subpanel to serve as a local shutoff means, something your panel requires you to provide yourself in this application, and partially because 240V stuff gobbles spaces twice as fast as normal. So, given that you're looking at $40 for the panel you specified (the $20 you spent on it already, as well as $15 for a 2-pole, 60A breaker and retainer kit to serve as a main disconnect at the shop, and another $5 for the PK7GTA ground bar you'll need), and going to a larger panel with a built-in main breaker (so no retainer kit) costs less than $100 more, including the larger accessory ground bar (for a HOM3060M200PC with a PK23GTA), I would simply return the panel you bought and pick up a much larger one. At minimum, I would use a 24-space, 100A or 125A, main breaker panel with this; you could even use a 200A panel here, if you would prefer to do so or wanted more spaces than are available in 100 or 125A.
Another thing you're missing is the grounding here. You'll need to run a 4-wire feeder (2 hots, a neutral, and a ground) to the subpanel, and fit an accessory ground bar kit to it as well as ensuring the green bonding screw is removed from the panel. With that done, you'll then need to run some #6 bare copper from the shed subpanel's grounding bus to a pair of 8' ground rods driven 8' apart, using an Arlington GC50 or equivalent to bring the grounding electrode conductor out of the panel. This is because the ground wire in the feeder provides a path for wayward utility electricity to get back to the utility (really, the transformer on the pole), while the ground rods provide a path for wayward natural electricity (induced voltages from lightning and such) to return to nature.
TORQUE ALL LUGS TO SPEC
Finally, you'll want to use an inch-pound torque wrench and/or torque screwdriver to tighten the various connector setscrews to their marked specification torques. This is required by 2017 NEC 110.14(D), as it ensures that your shed's electrical system will perform reliably for the long-haul, instead of giving you the loose lugnut!